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解答 - 几何数列

公比是：

r = - 0.29411764705882354

r=-0.29411764705882354

该系列的和是：

s = - 11

s=-11

此系列的通用形式是：

a_{n} = - 17 \cdot - {0.29411764705882354}^{n - 1}

a_n=-17*-0.29411764705882354^(n-1)

这个序列的第n项是：

- 17, 5, - 1.4705882352941178, 0.43252595155709345, - 0.12721351516385102, 0.037415739754073835, - 0.01100462933943348, 0.003236655688068671, - 0.0009519575553143151, 0.00027998751626891617

-17,5,-1.4705882352941178,0.43252595155709345,-0.12721351516385102,0.037415739754073835,-0.01100462933943348,0.003236655688068671,-0.0009519575553143151,0.00027998751626891617

查看步骤

逐步解答

1. 找到公比

通过将序列中的任何项除以前一项来找到公比：

$a_{2} a_{1} = \frac{5}{-} 17 = - 0.29411764705882354$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 0.29411764705882354$

2. 求和

5 个额外步骤

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

要找到系列的和，将第一项： $a = - 17$ 、公比： $r = - 0.29411764705882354$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = - 17 * ((1 - - {0.29411764705882354}^{2}) / (1 - - 0.29411764705882354))$

$s_{2} = - 17 * ((1 - 0.08650519031141869) / (1 - - 0.29411764705882354))$

$s_{2} = - 17 * (0.9134948096885813 / (1 - - 0.29411764705882354))$

$s_{2} = - 17 * (0.9134948096885813 / 1.2941176470588236)$

$s_{2} = - 17 \cdot 0.7058823529411764$

$s_{2} = - 11.999999999999998$

3. 找到通用形式

$a_{n} = a \cdot r^{n - 1}$

要找到系列的通用形式，将第一项： $a = - 17$ 和公比： $r = - 0.29411764705882354$ 插入几何级数的公式：

$a_{n} = - 17 \cdot - {0.29411764705882354}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = - 17$

$a_{2} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{2 - 1} = - 17 \cdot - {0.29411764705882354}^{1} = - 17 \cdot - 0.29411764705882354 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{3 - 1} = - 17 \cdot - {0.29411764705882354}^{2} = - 17 \cdot 0.08650519031141869 = - 1.4705882352941178$

$a_{4} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{4 - 1} = - 17 \cdot - {0.29411764705882354}^{3} = - 17 \cdot - 0.025442703032770204 = 0.43252595155709345$

$a_{5} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{5 - 1} = - 17 \cdot - {0.29411764705882354}^{4} = - 17 \cdot 0.007483147950814766 = - 0.12721351516385102$

$a_{6} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{6 - 1} = - 17 \cdot - {0.29411764705882354}^{5} = - 17 \cdot - 0.002200925867886696 = 0.037415739754073835$

$a_{7} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{7 - 1} = - 17 \cdot - {0.29411764705882354}^{6} = - 17 \cdot 0.0006473311376137341 = - 0.01100462933943348$

$a_{8} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{8 - 1} = - 17 \cdot - {0.29411764705882354}^{7} = - 17 \cdot - 0.000190391511062863 = 0.003236655688068671$

$a_{9} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{9 - 1} = - 17 \cdot - {0.29411764705882354}^{8} = - 17 \cdot 5.5997503253783236 E - 05 = - 0.0009519575553143151$

$a_{10} = a_{1} \cdot r^{n - 1} = - 17 \cdot - {0.29411764705882354}^{10 - 1} = - 17 \cdot - {0.29411764705882354}^{9} = - 17 \cdot - 1.646985389817154 E - 05 = 0.00027998751626891617$

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几何数列